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A stone is dropped into a quiet lake and waves move in circles at the speed of `5 cm//s`. At the instant when the radius of the circular wave is `8 cm`, how fast is the enclosed area increasing?A. `80 pi cm^(2)//s`B. `90 pi cm^(2)//s`C. `85 pi cm^(2)//s`D. `89 pi cm^(2)//s` |
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Answer» Correct Answer - A Enclosed area: `A= pi r^(2)` so `(dA)/(dt)=2pi r(dr)/(dt)` Here `r=8 cm, (dr)/(dt)=5 cm//s` `rArr (dA)/(dt)=(2pi) (8)(5)=80 pi cm^(2)//s` |
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